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Utilities for verified floating-point computation in Haskell: Controlled rounding, interval arithmetic, and affine arithmetic.

Haskell 67.90% C 32.10%
affine-arithmetic interval-arithmetic haskell

levitate's Issues

Question about multiplication

levitate/src/Affine.hs

Lines 226 to 244 in 8dfcf39

(*@) :: Affine -> Affine -> AffineMonad Affine
(*@) Empty _ = return Empty
(*@) _ Empty = return Empty
(*@) RealLine _ = return RealLine
(*@) _ RealLine = return RealLine
(*@) x@(Affine cx _) y@(Affine cy _) = do
let rx = radius x
let ry = radius y
let δ = rx *↑ ry
let p = (Interval.make cx cx) *! (Interval.make cy cy)
let δ' = δ +↑ (Interval.radius p)
aζ <- makeFreshAffine (-(Interval.midpoint p)) []
aδ <- makeFreshAffine δ' []
a1 <- cy ·@ x
a2 <- cx ·@ y
a3 <- a1 +@ a2
a4 <- a3 +@ aζ
a5 <- a4 +@ aδ
return a5

Hi,

as I understand from this piece of code, for two affines

x = x0 + x1 . e1
y = y0 + y1 . e2

their multiplication are calculated as:

z = x0y0 + y0x0 - x0y0 + y0x1e1 + x0y1e2 + |x1||y1|
  = (x0y0 + |x1||y1|) + y0x1e1 + x0y1e2

But by reading Stolffi reference, it should be:

z = x0y0  + y0x1e1 + x0y1e2 + |x1||y1|e3

In my tests your implementation seems to lead to more accurate results. Do you have any reference for that?

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